Birds spreading disease at feeders has been a mostly hidden, or under reported problem for a long time. Salmonella, aspergillosis, conjunctivitis, and avian pox are four of the worst offenders, but there are more. Sanitation is certainly one line of defense, but is seldom practiced. Just keeping a feeder filled is as much as most people are willing to do.
The most common way these diseases are transmitted from one bird to another is a sick bird eating at a feeder, defecating on seeds that have been dropped (whether in a tray or on the ground), and then other birds eating those seeds. Birds like chickadees, which take one seed away from the feeder and consume it there, are less commonly affected. House finches, gold finches, lessor goldfinches, grosbeaks and other species that stay at a feeder for lengthy periods while eating, are more susceptible.
It is somewhat helpful to never use a tray feeder where seeds commonly come into contact with feces, but then there is the problem of the seeds on the ground under the feeder. The longer they stay on the ground, the more likely they will be contaminated with pathogens from the feces of sick birds. At our home quail and jays remove the seeds nearly as quickly as they’re dropped, which may help, but a perfect solution is elusive.
Where possible, one could try putting a wire ‘cage’ on the ground under the feeder, made of 1/2” hardware cloth and perhaps 2 inches tall. The dropped seeds and feces will fall through this screen, but the birds can’t get to it. The accumulated mess would then need to be picked up and disposed of on a regular basis. This isn’t something that would work for a lot of situations, but it might for some.
Below is a good site that discusses diseases at bird feeders and suggested remedies.